I recently approached by a company that does not require internet at all but they wanted a network application to facilitate their production.
Is it possible to meet their requirement without the need of internet?
Yes, It's called an intRAnet and it's hosted on a web server inside the company network. You won't have as many firewall issues, and access to the internal databases will be easier. But otherwise, it's much the same - just no internet. I'm assuming that you are considering a browser-based application since the original question tag is "web-applications".
You could, of course, also write desktop applications with no browser necessary. Or there is the hybrid solution, Silverlight (or similar) or desktop app with web services on the back-end.
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